Skip Nav Destination
Close Modal
By
Adrian Pierorazio, Nicholas E. Cherolis, Michael Lowak, Daniel J. Benac, Matthew T. Edel
Search Results for
differential equations
Update search
Filter
- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References
Filter
- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References
Filter
- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References
Filter
- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References
Filter
- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References
Filter
- Title
- Authors
- Author Affiliations
- Full Text
- Abstract
- Keywords
- DOI
- ISBN
- EISBN
- Issue
- ISSN
- EISSN
- Volume
- References
NARROW
Format
Topics
Book Series
Date
Availability
1-20 of 54 Search Results for
differential equations
Follow your search
Access your saved searches in your account
Would you like to receive an alert when new items match your search?
Sort by
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001851
EISBN: 978-1-62708-241-9
... Ω m Ω t + Ω 2 t Equation 31 is thus a linear system of second-order differential equations, with time-dependent coefficients. Although there are no analytical solutions for such systems of equations, numerical methods of calculation are possible. A method known as spectral...
Abstract
Shaft misalignment and rotor unbalance contribute to the premature failure of many machine components. To understand how these failures occur and quantify the effects, investigators developed a model of a rotating assembly, including a motor, flexible coupling, driveshaft, and bearings. Equations of motion accounting for misalignment and unbalance were then derived using finite elements. A spectral method for resolving these equations was also developed, making it possible to obtain and analyze dynamic system response and identify misalignment and unbalance conditions.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003526
EISBN: 978-1-62708-180-1
... physical relationships of equilibrium/strain compatibility and material constitutive behavior/boundary conditions be satisfied. Classical theory of elasticity ( Ref 1 , 2 , 3 ) involves developing complex differential equations to satisfy these requirements, but such an approach is practical only...
Abstract
This article provides information on the development of finite element analysis (FEA) and describes the general-purpose applications of FEA software programs in structural and thermal, static and transient, and linear and nonlinear analyses. It discusses special-purpose finite element applications in piping and pressure vessel analysis, impact analysis, and microelectronics. The article describes the steps involved in the design process using the FEA. It concludes with two case histories that involve the use of FEA in failure analysis.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003516
EISBN: 978-1-62708-180-1
.... This may be accomplished using equations or computational mechanics (finite-element analysis). One needs to know the geometries and the materials as well as the processing history and mechanical properties of the materials. Thus far, this article has briefly discussed the mechanics, the structures...
Abstract
This article discusses the fundamental variables involved in fatigue-life assessment, which describe the effects and interaction of material behavior, geometry, and stress history on the life of a component. It compares the safe-life approach with the damage-tolerance approach, which employs the stress-life method of fatigue life assessment. The article examines the behavior of three different metallic materials used in the design and manufacture of structural components: steel, aluminum, and titanium. It also reviews the effects of retardation and spectrum load on component life. The article concludes with case studies of fatigue life assessment from the aerospace industry.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006773
EISBN: 978-1-62708-295-2
... relationships of equilibrium/strain compatibility and material constitutive behavior/boundary conditions be satisfied. Classical theory of elasticity ( Ref 1 – 3 ) involves developing complex differential equations to satisfy these requirements, but such an approach is practical only for situations where closed...
Abstract
When complex designs, transient loadings, and nonlinear material behavior must be evaluated, computer-based techniques are used. This is where the finite-element analysis (FEA) is most applicable and provides considerable assistance in design analysis as well as failure analysis. This article provides a general view on the applicability of finite-element modeling in conducting analyses of failed components. It highlights the uses of finite-element modeling in the area of failure analysis and design, with emphasis on structural analysis. The discussion covers the general development and both general- and special-purpose applications of FEA. The special-purpose applications of FEA covered are piping and pressure vessel analysis, impact analysis, and microelectronic and microelectromechanical systems analysis. The article provides case histories that involved the use of FEA in failure analysis.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
..., and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear...
Abstract
This article describes concepts and tools that can be used by the failure analyst to understand and address deformation, cracking, or fracture after a stress-related failure has occurred. Issues related to the determination and use of stress are detailed. Stress is defined, and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear elastic fracture mechanics analysis, with some mention of elastic-plastic fracture mechanics analysis. The article describes the probabilistic aspects of fatigue and fracture. Information on crack-growth simulation of the material is also provided.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003530
EISBN: 978-1-62708-180-1
... sign. Contemporary models to predict plastic deformation utilize the “flow” (i.e., yield) surface via the plastic potential equation. Because any linear model to predict flow (e.g., the Tresca criterion) is discontinuous in principal stress space, it cannot predict plastic strains for several loading...
Abstract
This article describes the underlying fundamentals, applications, the relevance and necessity of performing proper stress analysis in conducting a failure analysis. It presents an introduction to the stress analysis of bodies containing crack-like imperfections and the topic of fracture mechanics. The fracture mechanics approach is an important part of stress analysis at the tips of sharp cracks or discontinuities. The article reviews fracture mechanics concepts, including linear elastic fracture mechanics, elastic-plastic fracture mechanics, and subcritical fracture mechanics. It also provides information on the applications of fracture mechanics in failure analysis.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003517
EISBN: 978-1-62708-180-1
... are called “long-term” or “extended” overheating failures. Such a failure results from a relatively continuous extended period of slight overheating (differential between design and actual operating temperatures), a slowly increasing level of temperature or stress, or accumulation from several periods...
Abstract
This article focuses on the life assessment methods for elevated-temperature failure mechanisms and metallurgical instabilities that reduce life or cause loss of function or operating time of high-temperature components, namely, gas turbine blade, and power plant piping and tubing. The article discusses metallurgical instabilities of steel-based alloys and nickel-base superalloys. It provides information on several life assessment methods, namely, the life fraction rule, parameter-based assessments, the thermal-mechanical fatigue, coating evaluations, hardness testing, microstructural evaluations, the creep cavitation damage assessment, the oxide-scale-based life prediction, and high-temperature crack growth methods.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.9781627081801
EISBN: 978-1-62708-180-1
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006819
EISBN: 978-1-62708-329-4
Abstract
This article offers an overview of fatigue fundamentals, common fatigue terminology, and examples of damage morphology. It presents a summary of relevant engineering mechanics, cyclic plasticity principles, and perspective on the modern design by analysis (DBA) techniques. The article reviews fatigue assessment methods incorporated in international design and post construction codes and standards, with special emphasis on evaluating welds. Specifically, the stress-life approach, the strain-life approach, and the fracture mechanics (crack growth) approach are described. An overview of high-cycle welded fatigue methods, cycle-counting techniques, and a discussion on ratcheting are also offered. A historical synopsis of fatigue technology advancements and commentary on component design and fabrication strategies to mitigate fatigue damage and improve damage tolerance are provided. Finally, the article presents practical fatigue assessment case studies of in-service equipment (pressure vessels) that employ DBA methods.
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.process.c9001595
EISBN: 978-1-62708-235-8
... through-thickness distance hardness profile. The individual alloying element contributions and complicated regression equations typically used are included in ASTM A 255 and SAE J406. It has been demonstrated that almost all elements have a measurable effect on steel hardenability. Carbon has...
Abstract
Hardenability evaluation is typically applied to heat treatment process control, but can also augment standard metallurgical failure analysis techniques for steel components. A comprehensive understanding of steel hardenability is an essential complement to the skills of the metallurgical failure analyst. The empirical information supplied by hardenability analysis can provide additional processing and service insight to the investigator. The intent of this paper is to describe some applications of steel thermal response concepts in failure analysis, and several case studies are included to illustrate these applications.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003546
EISBN: 978-1-62708-180-1
... propagating into the substrate material of a thin-walled blade. Courtesy of Ashok Koul, Life Prediction Technologies, Inc. With this knowledge it should be possible to: Define the conditions for which empirical, experimentally based, life-prediction equations may be used Develop an appropriate...
Abstract
Thermomechanical fatigue (TMF) refers to the process of fatigue damage under simultaneous changes in temperature and mechanical strain. This article reviews the process of TMF with a practical example of life assessment. It describes TMF damages caused due to two possible types of loading: in-phase and out-of-phase cycling. The article illustrates the ways in which damage can interact at high and low temperatures and the development of microstructurally based models in parametric form. It presents a case study of the prediction of residual life in a turbine casing of a ship through stress analysis and fracture mechanics analyses of the casing.
Book Chapter
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006804
EISBN: 978-1-62708-329-4
... pressure-impulse diagrams, or closed-form energy equations that predict maximum responses of an equivalent single-degree-of-freedom or multi-degree-of-freedom system. Using these methods requires a selection of failure criteria, typically based on either ductility ratio or support rotation. Structures...
Abstract
This article addresses the effects of damage to equipment and structures due to explosions (blast), fire, and heat as well as the methodologies that are used by investigating teams to assess the damage and remaining life of the equipment. It discusses the steps involved in preliminary data collection and preparation. Before discussing the identification, evaluation, and use of explosion damage indicators, the article describes some of the more common events that are considered in incident investigations. The range of scenarios that can occur during explosions and the characteristics of each are also covered. In addition, the article primarily discusses level 1 and level 2 of fire and heat damage assessment and provides information on level 3 assessment.
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006823
EISBN: 978-1-62708-329-4
.... Alkire R. and Nicolaides G. , Differential Aeration Corrosion of a Passivating Metal under a Moist Film of Locally Variable Thickness , J. Electrochem. Soc. , Vol 121 ( No. 2 ), Feb 1974 , p 183 , 10.1149/1.2401778 11. Alkire R. and Nicolaides G. , The Existence...
Abstract
This article illustrates the use of the American Petroleum Institute (API) 579-1/ASME FFS-1 fitness-for-service (FFS) code (2020) to assess the serviceability and remaining life of a corroded flare knockout drum from an oil refinery, two fractionator columns affected by corrosion under insulation in an organic sulfur environment, and an equalization tank with localized corrosion in the shell courses in a chemicals facility. In the first two cases, remaining life is assessed by determining the minimum thickness required to operate the corroded equipment. The first is based on a Level 2 FFS assessment, while the second involves a Level 3 assessment. The last case involves several FFS assessments to evaluate localized corrosion in which remaining life was assessed by determining the minimum required thickness using the concept of remaining strength factor for groove-like damage and evaluating crack-like flaws using the failure assessment diagram. Need for caution in predicting remaining life due to corrosion is also covered.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006781
EISBN: 978-1-62708-295-2
... and approximate dimensions of the SSTG casing, including a schematic of the steam passageways where the majority of the service cracks were found during inspection. The SSTG start-up loading diagram is shown in Fig. 11(a) ( Ref 29 ). The transient temperature differentials computed for the initial loading...
Abstract
Thermomechanical fatigue (TMF) is the general term given to the material damage accumulation process that occurs with simultaneous changes in temperature and mechanical loading. TMF may couple cyclic inelastic deformation accumulation, temperature-assisted diffusion within the material, temperature-assisted grain-boundary evolution, and temperature-driven surface oxidation, among other things. This article discusses some of the major aspects and challenges of dealing with TMF life prediction. It describes the damage mechanisms of TMF and covers various experimental techniques to promote TMF damage mechanisms and elucidate mechanism coupling interactions. In addition, life modeling in TMF conditions and a practical application of TMF life prediction are presented.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003551
EISBN: 978-1-62708-180-1
... properties greatly influenced by temperature. Such an equation has often been used to describe the penetration of liquids in refractories without distinction between physical and chemical invasion. However, in the case of chemical invasion, the penetration-dissolution causes changes in composition (which...
Abstract
This article provides a discussion on the structural ceramics used in gas turbine components, the automotive and aerospace industries, or as heat exchangers in various segments of the chemical and power generation industries. It covers the fundamental aspects of chemical corrosion and describes the corrosion resistance characteristics of specific classes of refractories and structural ceramics. The article also examines the prevention strategies that minimize corrosion failures of both classes of materials.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003558
EISBN: 978-1-62708-180-1
... between polymers and metals. Wear also can be classified in relative terms as mild and severe. This classification is based on the nature of the wear, not the amount. The differentiation is primarily in terms of the features of the wear scars and secondarily by wear rate. Coarse features and high wear...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.steel.c9001149
EISBN: 978-1-62708-232-7
... lengths of rolled and welded COR-TEN steel plate butt welded together on site. The pipe sustained local buckling and cracking, then fractured during the first five months of operation. Failure was due to low cycle fatigue and fast fracture caused by differential thermal expansion stresses. Thermal lag...
Abstract
A large diameter steel pipe reinforced by stiffening rings with saddle supports was subjected to thermal cycling as the system was started up, operated, and shut down. The pipe functioned as an emission control exhaust duct from a furnace and was designed originally using lengths of rolled and welded COR-TEN steel plate butt welded together on site. The pipe sustained local buckling and cracking, then fractured during the first five months of operation. Failure was due to low cycle fatigue and fast fracture caused by differential thermal expansion stresses. Thermal lag between the stiffening rings welded to the outside of the pipe and the pipe wall itself resulted in large radial and axial thermal stresses at the welds. Redundant tied down saddle supports in each segment of pipe between expansion joints restrained pipe arching due to circumferential temperature variations, producing large axial thermal bending stresses. Thermal cycling of the system initiated fatigue cracks at the stiffener rings. When the critical crack size was reached, fast fracture occurred. The system was redesigned by eliminating the redundant restraints and by modifying the stiffener rings to permit free radial thermal breathing of the pipe.
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.power.c9001396
EISBN: 978-1-62708-229-7
... and corrosion will develop. In addition to being present as a surface film, magnetite in a soft powdery form is frequently found in boiler tubes as a corrosion product of iron and as such is often present in the pits and scabs which arise from normal corrosion, differential aeration corrosion, or deposit attack...
Abstract
The phenomenon of on-load corrosion is directly associated with the production of magnetite on the water-side surface of boiler tubes. On-load corrosion may first be manifested by the sudden, violent rupture of a boiler tube, such failures being found to occur predominantly on the fire-side surface of tubes situated in zones exposed to radiant heat where high rates of heat transfer pertain. In most instances, a large number of adjacent tubes are found to have suffered, the affected zone frequently extending in a horizontal band across the boiler. In some instances, pronounced local attack has taken place at butt welds in water-wall tubes, particularly those situated in zones of high heat flux. To prevent on-load corrosion an adequate flow of water must occur within the tubes in the susceptible regions of a boiler. Corrosion products and suspended matter from the pre-boiler equipment should be prevented from entering the boiler itself. Also, it is good practice to reduce as far as possible the intrusion of weld flash and other impedances to smooth flow within the boiler tubes.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... (or reliability) analysis depends on the number of failure equations required to describe the structural behavior. A system reliability analysis is required if a structure is composed of multiple components, has multiple failure modes, and/or has multiple failure locations, for example, multi-site damage. In each...
Abstract
This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering, selection of a probability distribution, the failure model definition, and a definition of the probability of failure. The article also explains the solution techniques for special cases and general solution techniques, such as first-second-order reliability methods, the advanced mean value method, the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006779
EISBN: 978-1-62708-295-2
... on the finite-life line, P R ( N R / S a R ), the equation of the finite-life line is: (Eq 5) N = N R · ( S a R / S a ) k where k is the slope of the finite-life line. The slope k is typically characterized by values between 3 and 15. A low slope corresponds...
Abstract
Fatigue failures may occur in components subjected to fluctuating (time-dependent) loading as a result of progressive localized permanent damage described by the stages of crack initiation, cyclic crack propagation, and subsequent final fracture after a given number of load fluctuations. This article begins with an overview of fatigue properties and design life. This is followed by a description of the two approaches to fatigue, namely infinite-life criterion and finite-life criterion, along with information on damage tolerance criterion. The article then discusses the characteristics of fatigue fractures followed by a discussion on the effects of loading and stress distribution, and material condition on the microstructure of the material. In addition, general prevention and characteristics of corrosion fatigue, contact fatigue, and thermal fatigue are also presented.